arXiv Machine Learning
Geometry-Agnostic Data-Driven Discovery of Extreme Scenarios
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When is a System Discoverable from Data? Discovery Requires Chaos
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Statistically Meaningful Geometry and Gauge Symmetry Breaking: A Geometric Foundation for Scientific Discovery and Intelligence Emergence
arXiv:2607. 05436v1 Announce Type: new Abstract: The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they merely sophisticated statistical pattern matchers?
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Physically-Relevant Information Learning in High-Dimensional Time-Derivatives Spaces
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Beyond the Ergodic Wall: A Discrete Geometric Physics Sandbox for Analysing AI Scaling Limits and Complexity Collapse
The paper identifies a fundamental limitation in current deep learning, describing an "ergodic ceiling" that forces models to converge to statistical averages of existing human knowledge. It proposes a discrete geometric physics sandbox—built on a Holographic E8 Projection Engine and a lattice of Planck‑scale spheres—to inject non‑ergodic, path‑dependent insight and enforce thermodynamic constraints. By modeling spacetime as nested FCC lattices and using topological constraints, the sandbox aims to prevent model collapse, recover quantum mechanics via renormalisation‑group flows, and potentially collapse NP‑to‑P complexity by restricting algorithmic search to physically conserved trajectories.
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How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit
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Learning Chaos Without Seeing Chaos: Extrapolation of Global Dynamics in Autoregressive Transformers
Autoregressive transformers trained on limited trajectories of nonlinear dynamical systems can extrapolate to unseen parameter regimes, reproducing period-doubling cascades, chaotic dynamics, and attractor structures with high fidelity. In the logistic map, the model captures successive period doublings up to period 128, achieving a scaling ratio within $5 imes10^{-4}$ of the Feigenbaum constant. The study also shows how control‑parameter information is processed via attention, shaping the closed‑loop dynamics during training.